Charge acquired by a spherical ball bouncing on an electrode: comparison between theory and experiment

A conducting ball immersed in a poorly conducting liquid between two horizontal plates acquires a charge when subjected to a dc voltage. When the applied voltage is high enough for the electric force to overcome gravity, the ball rises, moves up through the liquid and falls down as its charge leaks away. The threshold of voltage, as well as the time of flight between contacts, depends on the charge acquired by the ball during the contact with the electrode. Experiments have been done using liquids of different conductivities and it was shown that the conductivity does not affect the lift-off voltage. When the ball gets close to the electrode a discharge occurs and a current pulse is registered by the external circuit. The charge carried by the pulse is an order of magnitude smaller than the charge transferred to the ball from the electrode. We have made a detailed study, with different balls and liquids, of the charge transferred to the external circuit. The dependence on the different parameters of the ratio charge transferred to the circuit-charge acquired by the ball is explained using the coefficients of capacity of the electrostatic system.